Regular partitions of gentle graphs

Szemerédi's Regularity Lemma is a very useful tool of extremal combinatorics. Recently, several refinements of this seminal result were obtained for special, more structured classes of graphs. We survey these results in their rich combinatorial context. In particular, we stress the link to the...

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Bibliographic Details
Published inActa mathematica Hungarica Vol. 161; no. 2; pp. 719 - 755
Main Authors Jiang, Y., Nešetřil, J., Ossona de Mendez, P., Siebertz, S.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.08.2020
Springer Nature B.V
Springer Verlag
Subjects
Combinatorial analysis
Combinatorics
Graphs
Mathematics
Mathematics and Statistics
Regularity
regularity lemma
order dimension
05C75
sparsity
03C98
03C45
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Summary:Szemerédi's Regularity Lemma is a very useful tool of extremal combinatorics. Recently, several refinements of this seminal result were obtained for special, more structured classes of graphs. We survey these results in their rich combinatorial context. In particular, we stress the link to the theory of (structural) sparsity, which leads to alternative proofs, refinements and solutions of open problems. It is interesting to note that many of these classes present challenging problems. Nevertheless, from the point of view of regularity lemma type statements, they appear as ``gentle'' classes.
ISSN:0236-5294
1588-2632
DOI:10.1007/s10474-020-01074-x